Related papers: Controllability and necessary second-order optimal…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
We systematically introduce an approach to the analysis and (numerical) solution of a broad class of nonlinear unconstrained optimal control problems, involving ordinary and distributed systems. Our approach relies on exact representations…
Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).
For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
In the paper we consider the infinite horizon control problems on the interval with free right-hand endpoint. We obtain the necessary conditions of strict optimality. The method of the proof actually follows the classic paper by Halkin, and…
This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by…
We study two notions of controllability on a parabolic system with coupling terms of order one. Based on existing results on, on one side parabolic systems with coupling terms of order zero, and on the other one parabolic systems with…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
Control systems involving unknown parameters appear a natural framework for applications in which the model design has to take into account various uncertainties. In these circumstances the performance criterion can be given in terms of an…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
This paper establishes a unified framework connecting local controllability, necessary conditions for optimality, and attainability in free-time optimal control problems. The central object of our investigation is the $\Lambda$-set, which…
This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…
In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization…
In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
In the present paper we deal with an optimal control problem related to a model in population dynamics; more precisely, the goal is to modify the behavior of a given density of individuals via another population of agents interacting with…
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…